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Description of the Transistor Gyrator
The circuit shown is a transistor-based gyrator, an active network that makes a capacitor behave like an inductor when viewed from the input node. Instead of using an operational amplifier, this design uses two bipolar junction transistors (BJTs) to achieve the same impedance transformation.
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1. Purpose and general behavior
From the left-hand input node, the circuit presents an impedance that increases with frequency, which is the defining characteristic of an inductance. No physical coil is present; the inductive behavior is synthesized using a small capacitor, resistors, and active devices.
This type of gyrator is especially useful at low and audio frequencies, where real inductors would be large, lossy, or expensive.
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2. Input network
The signal enters through a 10 kΩ resistor, which isolates the source and sets the interaction between the source impedance and the simulated inductance.
A 100 nF capacitor to ground provides AC coupling and establishes a reference for low-frequency behavior, preventing DC from disturbing the biasing of the transistors.
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3. Gyrating capacitor
The key reactive element is the 22 nF capacitor connected between the input node and the base of the first transistor.
This capacitor is the element whose behavior is transformed into that of an inductor. Its current is controlled and “reflected” by the transistor stages so that, from the input perspective, it behaves as if current were flowing through a coil.
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4. First transistor stage
The first transistor operates as a voltage-controlled current device.
Small changes in voltage at its base, driven through the 22 nF capacitor, cause proportional changes in collector and emitter currents. The 100 kΩ resistor connected to its emitter sets the operating current and contributes to defining the effective inductance.
This stage senses the capacitor current and converts it into a controlled current signal.
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5. Second transistor stage
The second transistor acts as a current buffer and gain stage.
Its emitter resistor of 2.2 kΩ establishes a stable bias current and scales the current coming from the first transistor. The two transistors together behave as a compound active element with high effective transconductance, similar in role to an operational amplifier in op-amp gyrators.
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6. Power supply and load isolation
The circuit is powered from ±10 V supplies, allowing symmetrical signal swing and linear operation around ground.
A 560 Ω resistor connected to the supply provides collector load and further stabilizes the operating point, while isolating the gyrator action from supply variations.
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7. Inductive behavior and tuning
The effective inductance seen at the input depends mainly on
the value of the 22 nF capacitor
the transconductance of the transistors
the emitter resistors (100 kΩ and 2.2 kΩ)
Increasing the capacitor value or the effective gain of the transistor stages increases the apparent inductance. Decreasing them has the opposite effect.
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8. Frequency limits and realism
At low frequencies, the circuit closely approximates an ideal inductor.
At higher frequencies, non-ideal effects appear due to
finite transistor gain
base-emitter capacitances
parasitic resistances
Compared to op-amp gyrators, transistor gyrators generally operate over a narrower frequency range but require fewer components and no integrated amplifiers.
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9. Typical applications
Audio-frequency filters and resonators
Inductor replacement in analog signal processing
Educational demonstrations of impedance transformation
Circuits where op amps are unavailable or undesirable
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Summary
This transistor gyrator uses two BJTs and a capacitor to simulate inductive behavior. The first transistor senses and converts the capacitor current, while the second buffers and scales it. Together, they cause the input node to behave as if it were connected to an inductor, providing a practical alternative to physical coils at low frequencies.
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